Groups elementarily equivalent to metabelian Baumslag-Solitar groups and regular bi-interpretability

2024/06/30 by Evelina Daniyarova, Daniyarova, Evelina, Alexei Myasnikov +1
Mathematics · #math.GR #math.LO

paper · pdf · doi:10.48550/arxiv.2407.00642

Abstract

We prove that metabelian Baumslag-Solitar group BS(1,k), k>1, is (strongly) regularly bi-interpretable with the ring of integers ℤ, and describe in algebraic terms all groups that are elementarily equivalent to BS(1,k).

Related

• Two Remarks on First-Order Theories of Baumslag-Solitar Groups
• Bi-interpretability with ℤ and models of the complete elementary theories of SL_n(O), T_n(O) and GL_n(O), n≥ 3
• Commensurability and bi-interpretability of groups
• The BNS invariants of the generalized solvable Baumslag-Solitar groups and of their finite index subgroups
• Direct and Inverse Problems in Baumslag-Solitar Group BS(1,3)